Handbook of Categorical Algebra : Volume 1, Basic Category Theory

Francis Borceux
Cambridge University Press

A Handbook of Categorical Algebra, in three volumes, is a detailed account of everything a mathematician needs to know about category theory. Each volume is self-contained and is accessible to graduate.

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students with a good background in mathematics. Volume 1 is devoted to general concepts. After introducing the terminology and proving the fundamental results concerning limits, adjoint functors and Kan extensions, the categories of fractions are studied in detail; special consideration is paid to the case of localizations. The remainder of the first volume studies various "refinements" of the fundamental concepts of category and functor.